Equivalent particle sizes

Averages

The averages marked on the frequency distribution curve.

Methods of presenting data of particle size distribution measurements

The powder consisting of particles of relatively homogeneous size is usually known as a monodispersion; the powder consisting of particles of heterogeneous size covering a wide size range is known as a polydispersion. In general a curve of size distribution is often steeply sided towards the smaller sizes , and consequently found to be an asymmetric curve with a tail that extends far towards the large sizes.

Particle size distribution of an unmilled zirconia-yttria powder.

Particle size distribution of the powder after attrition milling.

Model Distribution Functions

Normal Distribution

Log-Normal Distribution

Rosin-Rammler Distribution

F(x) is a mass percent of the particles larger than a given size. The mean size is the size at 36.8% of the distribution, written as x36.8 or d0. The measure of width of the distribution is n. The value of n can be read from linearized Rosin-Rammler distribution as a slope of the straight line.

A – powdered glass in the CaO-B2O3-SiO2 system, ball-milled, B - α-Al2O3 powder, milled in a ring-mill, C – 6.5 mol % Y2O3-ZrO2 s.s. powder calcined at 800oC, D – hydrothermally crystallized powder of NiFe2O4.

In general, particles prepared by the solution techniques, especially precipitation methods, are found to have a size distribution that fits a log-normal distribution. Powders prepared by comminution are frequently described by the Gaudin, Schuhmann and Rosin-Rammler laws. Powder characterization

Weighted distributions

Particle size and shape It is difficult to express the shape and size of powder particles because the powder is generally composed of inhomogeneous particles of differing shapes and sizes. Various terms for expressing different shapes verbally are given in a table below. However, these terms for describing different shapes seem not to be well enough defined.

If the particles in a powder are of approximately the same size and geometrical shape such as spherical, cubical or rod-like, a representative size of the particles can be given as the diameter or the length of a side. But if the particles are of heterogeneous shape, then it may be difficult to decide on the representative size.

Equivalent projected diameters (completion)

Shape indices

One of the simplest definition of particle shape is that due to Wadell (1932), who defined sphericity, ψ, as

Sampling

Fractal analysis

Ble

ndin

g po

wde

r sam

ples

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